Practice Problems: 1. A price war: 1A. Consider a pair of duopolists engaged in price competition. Suppose that each duopolist can produce output at a cost of $4 per unit: AC=MC=$4. Furthermore, each firm has only two pricing options: charge a high price of $8 or charge a low price of $6. If both firms set high prices, each can expect to sell 2.5 million units annually. If both set low prices, each firm's sales increase to 3.5 million units. Finally, if one firm sets a high price and the other a low price, the former sells 1.25 million units, the latter 6 million units. Show a payoff table summarizing the profit implications of the firm's different pricing strategies.

Suppose that some consumers display a strong brand allegiance for one firm or the other. Consequently, any price difference between the duopolists is expected to produce a much smaller swing in the firms' market shares. Specifically, suppose that if one firm charges a price of $6 and the other $8, the former sells 4 million units and the latter 2 million instead of the original 6 million and 1.25 million sales). All other facts are as before. How does this change the payoffs? What price should each firm set? Explain.​